Coke or Pepsi? Alexandra V. Garrison Austin M. Lewis Math 005--Chance Goals On campus, Coca-Cola machines are in all of the dorms and sold in DDS establishments. We want to determine whether there is a difference between Coke and Pepsi. We more importantly want to see whether Dartmouth students prefer Coke to Pepsi. Our Pre-Test Thoughts We think that most students can tell the difference between Coke and Pepsi. We also believe that most students will prefer Coke because it is so present on campus. Our prediction is that 80 percent of students will prefer Coke. We also believe that they will be able to determine which is Pepsi and which is Coke. Other Thoughts…. We thought that it would be an overwhelming preference (80% or higher) because there are less options for Pepsidrinkers. p=0.8 was our power Coke or Pepsi? The Actual Test We gave each subject a sample of Coke and a sample of Pepsi without them knowing which one is which. We asked if they tasted a difference. If they detected a difference, we asked which did they prefer. Then we asked them to identify which they thought was Coke. Null Hypothesis Our null hypothesis supports the idea that most of our subjects will be able to taste a difference. The subjects are like a fair coin; they are just as likely to pick Coke as they are likely to pick Pepsi. p=0.5 Alternate Hypothesis Dartmouth students will prefer Coke over Pepsi. Because Coke is so readily available on campus, our administration would invest in a company that students prefer. p>0.5 Our Binomial Distribution 0.16 0.14 0.12 0.1 Probability Under Null 0.08 Probability Under Power Hypothesis 0.06 0.04 0.02 0 1 5 9 13 17 21 25 29 33 37 41 45 49 Data Data Chart A #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #26 #27 #28 #29 #30 #31 #32 #33 #34 #35 #36 #37 #38 #39 #40 #41 #42 #43 #44 #45 #46 #47 #48 #49 #50 Year 03, 04, 05, 06, 07 6 6 7 7 7 7 7 5 5 5 7 7 6 7 7 7 7 6 5 7 7 7 7 7 6 4 6 6 4 7 7 5 4 6 7 6 7 7 7 4 7 7 6 4 4 4 7 7 7 7 Gender m, f m m f m m f f f m m m f m f m f f f m f m m m m m f m f f f f m f f f f m f m m f f f m m f m f m f Question #1 Question #2 yes, no right, left, other yes left no n/a yes left yes other yes right yes left yes left yes right no n/a yes right no n/a yes left yes left yes left yes left yes left yes right yes right no n/a yes right no n/a no n/a yes right no n/a yes other yes left yes right yes right yes right yes right yes other yes left yes right no n/a yes right yes left yes right yes left yes right yes left yes left yes left no n/a yes left yes right no n/a yes right yes left yes left yes left Question #3 right, left, other left n/a right left right left right left n/a left n/a other right right right left left right n/a left n/a n/a right n/a left left right left right left right right right n/a left left right left right left left left n/a left right n/a right left left left The Percentage Breakdown Coke=60% Pepsi=32.5% No preference=7.5% Our Results 80% of the subjects were able to distinguish the difference between Coke and Pepsi. Eighty-six percent of our subjects had a preference….. But of those who did only 60% preferred Coke. This is significantly lower than our original belief of 80%. Actual Z-score z-score = Pactutal – Pnull √Pnull (1- Pnull) N 0.6 – 0.5 √(0.5)2 = 1.265 40 With a confidence level of 95%, our z-score would have had to have been 1.65 to be able to reject the null hypothesis Z-score of hypothesis We calculated our original z- score to be 3.162. With this score, the chance that 80% of students prefer Coke is 1/1000 This shows that our test was not very powerful so we should have had a smaller power hypothesis Critical Region Our critical region at the 5% level is P ≥ 0.6202 Unfortunately, our P = 0.6 so we must assume that more students chose Coke over Pepsi due to chance. Decision: Null or Alternate? In the end, we found that we had to reject our alternate hypothesis. A Type I error ocurred Our Analysis a Type I error occurred in which we had to reject our alternate hypothesis and we were forced to accept our null hypothesis Because of our results, we cannot accurately assume that Dartmouth students prefer Coke, despite Coke’s abundance on campus Confounding Factors Inadequate pallet cleansers, ie. Lays Potato Chips, the salt hindered our subjects from tasting objectively. It was not completely randomly selected. Even though we asked many strangers to participate in our test, there were quite a few of our subjects who are friends.